A quasi-linear estimation method--Application to Kalman filtering with stochastic regressors

An estimation method, called quasi-linear estimation, is presented. Quasi-linear estimation is aimed to give an intermediate possibility between linear and nonlinear estimation. A quasi-linear estimator of a parameter vector a given two observation vectors and is defined to be of the form , where the vector and the matrix are -measurable. Orthogonal projections are used to derive the quasi-linear minimum mean square error estimator. This estimator is . Quasi-linear estimation is applied to derive a Kalman type filter for discrete-time dynamic linear models with stochastic regressors.